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The asymmetric unit of the title compound, [Ni(C4H13N3)(C6H8N3O2)]I·H2O, comprises a six-coordinated Ni(II) complex cation, an I- anion, and one water molecule of crystallization. Intermolecular hydrogen bonds link the complex cations into extended two-dimensional layers.

Supporting information

cif

Crystallographic Information File (CIF) https://doi.org/10.1107/S1600536802006116/bt6133sup1.cif
Contains datablocks global, I

hkl

Structure factor file (CIF format) https://doi.org/10.1107/S1600536802006116/bt6133Isup2.hkl
Contains datablock I

CCDC reference: 185750

Key indicators

  • Single-crystal X-ray study
  • T = 293 K
  • Mean [sigma](C-C) = 0.004 Å
  • R factor = 0.022
  • wR factor = 0.051
  • Data-to-parameter ratio = 19.1

checkCIF results

No syntax errors found

ADDSYM reports no extra symmetry


Yellow Alert Alert Level C:
ABSTM_02 Alert C The ratio of expected to reported Tmax/Tmin(RR) is > 1.10 Tmin and Tmax reported: 0.322 0.483 Tmin and Tmax expected: 0.249 0.427 RR = 1.142 Please check that your absorption correction is appropriate. PLAT_420 Alert C D-H Without Acceptor N2 - H2D ? PLAT_420 Alert C D-H Without Acceptor N3 - H3C ? General Notes
ABSTM_02 When printed, the submitted absorption T values will be replaced by the scaled T values. Since the ratio of scaled T's is identical to the ratio of reported T values, the scaling does not imply a change to the absorption corrections used in the study. Ratio of Tmax expected/reported 0.884 Tmax scaled 0.427 Tmin scaled 0.284
0 Alert Level A = Potentially serious problem
0 Alert Level B = Potential problem
3 Alert Level C = Please check

Comment top

Previously we have reported the crystal structures of a series of amino acidato complexes with the formula [M(N4)(amino acidato)]n+, where N4 = triethylenetetraamine (trien) or tris(2-aminoethyl)amine (tren), M = Co3+, n = 2+ and M = Ni2+, n = 1+ (Cai et al., 2000, 2001, 2002; Hu et al., 2001). Their interesting packing arrangements directed by intermolecular hydrogen bonds were also discussed. Compared with the cobalt(III) analogues, structures of Ni(II) amino acidato complexes are less well documented (Cai et al., 2002).

In the title compound, Ni(II) is six-coordinated by three nitrogen atoms of the diethylenetriamine (dien) ligand, two N atoms and one O atom of the histidine ligand, as shown in Fig.1. Histidine is a potential multidentate ligand displaying varying coordination modes in different chemical environments. In the reported compond [Co(trien)(histidinato)](ClO4)2·2H2O (Hu et al., 2001), histidine is coordinated to Co(III) through one of the imidazol nitrogen atoms and the amino N atom. There are only two structures in the Cambridge Structural Database (Allen & Kennard, 1993) showing the tridentate coordination mode of histidine with Ni(II), namely [Ni(histidinato)(SCN)(H2O)2]·H2O (Shvelashvili et al., 1980, 1984; Sakurai et al., 1978) and [Ni(histidinato)2]·H2O (Shvelashvili et al., 1984; Sakurai et al., 1978). The bond lengths and angles of the Ni(II) coordination geometry in (I) are in agreement with these structures. The C–O bond lengths of the carboxylate group are 1.269 (3) and 1.235 (3) Å respectively, indicative of conjugated bonds.

As shown in Fig.2, the catonic complex is connected to another one, related by an inversion center, through complementary hydrogen bonds, formed by the free carboxylate oxygen atoms and the amino hydrogen atoms of both the dien and histidine ligands, leading to racemic pairs. These racemic pairs are further linked to each other via hydrogen bonds formed by the free carboxylate oxygen and the imidazol amino hydrogen and form an extended two-dimensional network along the bc plane. Both the crystalline water molecule and I- are involved in extensive hydrogen bonding with the cation, as shown in Table 1.

Experimental top

I was obtained by the method described elsewhere (Cai et al., 2002).

Refinement top

All hydrogen atoms of the ligands were placed in idealized positions and refined as riding atoms with with fixed individual displacement parameters [U(H) = 1.2 Ueq(N), U(H) = 1.2 Ueq(C)]. Hydrogen atoms of the water molecules were located from the difference Fourier map. Their coordinates were not refined but their displacement parameters.

Computing details top

Data collection: SMART (Bruker, 1998); cell refinement: SMART; data reduction: SAINT-Plus (Bruker, 1999); program(s) used to solve structure: SHELXS97 (Sheldrick, 1997); program(s) used to refine structure: SHELXL97 (Sheldrick, 1997); molecular graphics: SHELXTL (Bruker, 1998 ); software used to prepare material for publication: SHELXTL.

Figures top
[Figure 1] Fig. 1. Contents of the asymmetric unit showing 30% probability displacement ellipsoids.
[Figure 2] Fig. 2. Packing arrangement of the cations. Iodide, water of hydration and hydrogen atoms attached to carbons are omitted for clarity.
(diethylenetriamine-N,N',N'')(DL-histinato-N,N',O)nickel(II) iodide monohydrate top
Crystal data top
[Ni(C4H13N3)(C6H8N3O2)]I·H2OF(000) = 920
Mr = 460.95Dx = 1.775 Mg m3
Monoclinic, P21/nMo Kα radiation, λ = 0.71073 Å
a = 9.384 (5) ÅCell parameters from 813 reflections
b = 15.323 (7) Åθ = 2.9–25.3°
c = 12.667 (6) ŵ = 2.93 mm1
β = 108.758 (8)°T = 293 K
V = 1724.6 (14) Å3Block, purple
Z = 40.50 × 0.41 × 0.29 mm
Data collection top
CCD area detector
diffractometer
3673 independent reflections
Radiation source: fine-focus sealed tube3280 reflections with I > 2σ(I)
Graphite monochromatorRint = 0.018
phi and ω scansθmax = 27.0°, θmin = 2.2°
Absorption correction: multi-scan
(SADABS: Sheldrick, 1996; Blessing, 1995)
h = 117
Tmin = 0.322, Tmax = 0.483k = 1917
9823 measured reflectionsl = 1616
Refinement top
Refinement on F2Primary atom site location: structure-invariant direct methods
Least-squares matrix: fullSecondary atom site location: difference Fourier map
R[F2 > 2σ(F2)] = 0.022Hydrogen site location: inferred from neighbouring sites
wR(F2) = 0.051H atoms treated by a mixture of independent and constrained refinement
S = 1.08 w = 1/[σ2(Fo2) + (0.0191P)2 + 1.0794P]
where P = (Fo2 + 2Fc2)/3
3673 reflections(Δ/σ)max = 0.002
192 parametersΔρmax = 0.60 e Å3
0 restraintsΔρmin = 0.68 e Å3
Crystal data top
[Ni(C4H13N3)(C6H8N3O2)]I·H2OV = 1724.6 (14) Å3
Mr = 460.95Z = 4
Monoclinic, P21/nMo Kα radiation
a = 9.384 (5) ŵ = 2.93 mm1
b = 15.323 (7) ÅT = 293 K
c = 12.667 (6) Å0.50 × 0.41 × 0.29 mm
β = 108.758 (8)°
Data collection top
CCD area detector
diffractometer
3673 independent reflections
Absorption correction: multi-scan
(SADABS: Sheldrick, 1996; Blessing, 1995)
3280 reflections with I > 2σ(I)
Tmin = 0.322, Tmax = 0.483Rint = 0.018
9823 measured reflections
Refinement top
R[F2 > 2σ(F2)] = 0.0220 restraints
wR(F2) = 0.051H atoms treated by a mixture of independent and constrained refinement
S = 1.08Δρmax = 0.60 e Å3
3673 reflectionsΔρmin = 0.68 e Å3
192 parameters
Special details top

Geometry. All e.s.d.'s (except the e.s.d. in the dihedral angle between two l.s. planes) are estimated using the full covariance matrix. The cell e.s.d.'s are taken into account individually in the estimation of e.s.d.'s in distances, angles and torsion angles; correlations between e.s.d.'s in cell parameters are only used when they are defined by crystal symmetry. An approximate (isotropic) treatment of cell e.s.d.'s is used for estimating e.s.d.'s involving l.s. planes.

Refinement. Refinement of F2 against ALL reflections. The weighted R-factor wR and goodness of fit S are based on F2, conventional R-factors R are based on F, with F set to zero for negative F2. The threshold expression of F2 > σ(F2) is used only for calculating R-factors(gt) etc. and is not relevant to the choice of reflections for refinement. R-factors based on F2 are statistically about twice as large as those based on F, and R- factors based on ALL data will be even larger.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Å2) top
xyzUiso*/Ueq
I10.363034 (18)0.103023 (10)0.688563 (14)0.04352 (6)
Ni10.79822 (3)0.915238 (16)0.75632 (2)0.02584 (7)
N10.9742 (2)0.98089 (12)0.71850 (14)0.0328 (4)
H1C1.01811.01970.77380.039*
N20.6680 (2)0.97424 (13)0.60666 (15)0.0380 (4)
H2C0.65680.93790.54880.046*
H2D0.57620.98820.60970.046*
N30.8878 (2)0.80687 (12)0.69617 (15)0.0336 (4)
H3C0.92630.76860.75200.040*
H3D0.81400.77990.64250.040*
N40.7454 (2)1.01534 (11)0.85211 (14)0.0306 (4)
H4C0.81371.05860.86470.037*
H4D0.65371.03750.81670.037*
N50.4510 (2)0.74343 (13)0.75751 (18)0.0442 (5)
H5B0.39290.69990.73050.053*
N60.6226 (2)0.84410 (12)0.77719 (15)0.0337 (4)
C10.9110 (3)1.02831 (16)0.61223 (19)0.0418 (5)
H1A0.91660.99180.55120.050*
H1B0.96981.08050.61320.050*
C20.7500 (3)1.05306 (17)0.5943 (2)0.0459 (6)
H2A0.74481.09660.64850.055*
H2B0.70551.07750.52030.055*
C31.0063 (3)0.83522 (16)0.6509 (2)0.0428 (5)
H3A0.96220.84970.57260.051*
H3B1.07800.78830.65740.051*
C41.0854 (3)0.91398 (16)0.7147 (2)0.0424 (5)
H4A1.14370.89700.79000.051*
H4B1.15390.93780.67890.051*
C50.7486 (2)0.97372 (13)0.95797 (16)0.0303 (4)
H5A0.76171.01921.01470.036*
C60.8836 (2)0.91176 (12)0.99501 (17)0.0293 (4)
C70.6011 (3)0.92577 (16)0.94445 (19)0.0381 (5)
H7A0.60540.90241.01660.046*
H7B0.52010.96820.92350.046*
C80.5610 (2)0.85304 (14)0.86167 (18)0.0326 (4)
C90.5533 (3)0.77723 (15)0.71655 (19)0.0397 (5)
H9A0.57310.75650.65370.048*
C100.4551 (3)0.79035 (16)0.8500 (2)0.0439 (6)
H10A0.39670.78110.89600.053*
O10.93527 (18)0.88474 (10)0.91983 (12)0.0350 (3)
O20.9352 (2)0.89227 (10)1.09468 (12)0.0395 (4)
O1W0.1850 (2)0.78154 (13)0.99661 (15)0.0572 (5)
HW10.09930.81230.97200.087 (12)*
HW20.15240.73520.94960.085 (12)*
Atomic displacement parameters (Å2) top
U11U22U33U12U13U23
I10.03620 (9)0.04348 (10)0.04843 (10)0.00282 (6)0.01021 (7)0.00072 (6)
Ni10.02600 (14)0.02975 (13)0.02187 (13)0.00023 (10)0.00783 (10)0.00186 (9)
N10.0315 (9)0.0380 (10)0.0280 (9)0.0049 (8)0.0084 (7)0.0035 (7)
N20.0326 (10)0.0525 (12)0.0260 (9)0.0051 (9)0.0056 (8)0.0006 (8)
N30.0340 (10)0.0349 (10)0.0324 (9)0.0008 (8)0.0113 (8)0.0032 (7)
N40.0322 (9)0.0282 (8)0.0276 (9)0.0038 (7)0.0046 (7)0.0007 (7)
N50.0399 (11)0.0397 (11)0.0529 (12)0.0138 (9)0.0146 (10)0.0089 (9)
N60.0350 (10)0.0339 (9)0.0359 (10)0.0054 (8)0.0167 (8)0.0082 (7)
C10.0495 (14)0.0435 (13)0.0353 (12)0.0054 (11)0.0177 (11)0.0057 (10)
C20.0555 (16)0.0473 (14)0.0346 (12)0.0079 (12)0.0141 (11)0.0117 (10)
C30.0431 (14)0.0470 (14)0.0455 (13)0.0049 (11)0.0242 (11)0.0046 (11)
C40.0285 (12)0.0525 (14)0.0485 (14)0.0011 (10)0.0156 (10)0.0015 (11)
C50.0366 (11)0.0286 (10)0.0248 (10)0.0021 (8)0.0089 (9)0.0058 (8)
C60.0345 (11)0.0249 (10)0.0264 (10)0.0023 (8)0.0067 (9)0.0019 (7)
C70.0397 (13)0.0446 (12)0.0359 (12)0.0025 (10)0.0203 (10)0.0063 (10)
C80.0292 (11)0.0370 (11)0.0339 (11)0.0013 (9)0.0135 (9)0.0013 (9)
C90.0418 (13)0.0386 (12)0.0403 (12)0.0067 (10)0.0156 (11)0.0099 (10)
C100.0391 (13)0.0486 (14)0.0497 (14)0.0061 (11)0.0224 (11)0.0012 (11)
O10.0381 (8)0.0399 (8)0.0259 (7)0.0117 (7)0.0087 (6)0.0024 (6)
O20.0531 (10)0.0373 (8)0.0240 (7)0.0041 (7)0.0067 (7)0.0033 (6)
O1W0.0542 (11)0.0668 (13)0.0436 (10)0.0238 (10)0.0060 (9)0.0018 (9)
Geometric parameters (Å, º) top
Ni1—N62.0621 (19)C1—C21.503 (4)
Ni1—N22.1011 (19)C1—H1A0.9700
Ni1—O12.1092 (17)C1—H1B0.9700
Ni1—N42.1111 (18)C2—H2A0.9700
Ni1—N32.1111 (19)C2—H2B0.9700
Ni1—N12.1162 (19)C3—C41.508 (3)
N1—C41.474 (3)C3—H3A0.9700
N1—C11.476 (3)C3—H3B0.9700
N1—H1C0.9100C4—H4A0.9700
N2—C21.467 (3)C4—H4B0.9700
N2—H2C0.9000C5—C71.527 (3)
N2—H2D0.9000C5—C61.531 (3)
N3—C31.471 (3)C5—H5A0.9800
N3—H3C0.9000C6—O21.235 (3)
N3—H3D0.9000C6—O11.269 (3)
N4—C51.476 (3)C7—C81.493 (3)
N4—H4C0.9000C7—H7A0.9700
N4—H4D0.9000C7—H7B0.9700
N5—C91.334 (3)C8—C101.356 (3)
N5—C101.365 (3)C9—H9A0.9300
N5—H5B0.8600C10—H10A0.9300
N6—C91.320 (3)O1W—HW10.8967
N6—C81.377 (3)O1W—HW20.9144
N6—Ni1—N294.94 (8)N1—C1—H1B109.5
N6—Ni1—O190.98 (7)C2—C1—H1B109.5
N2—Ni1—O1167.26 (7)H1A—C1—H1B108.1
N6—Ni1—N488.03 (7)N2—C2—C1108.2 (2)
N2—Ni1—N491.72 (8)N2—C2—H2A110.1
O1—Ni1—N477.19 (7)C1—C2—H2A110.1
N6—Ni1—N393.31 (8)N2—C2—H2B110.1
N2—Ni1—N3101.33 (8)C1—C2—H2B110.1
O1—Ni1—N389.56 (7)H2A—C2—H2B108.4
N4—Ni1—N3166.71 (7)N3—C3—C4109.31 (18)
N6—Ni1—N1173.81 (7)N3—C3—H3A109.8
N2—Ni1—N182.02 (8)C4—C3—H3A109.8
O1—Ni1—N193.09 (7)N3—C3—H3B109.8
N4—Ni1—N197.42 (8)C4—C3—H3B109.8
N3—Ni1—N182.06 (8)H3A—C3—H3B108.3
C4—N1—C1113.19 (18)N1—C4—C3110.04 (19)
C4—N1—Ni1106.77 (14)N1—C4—H4A109.7
C1—N1—Ni1109.06 (14)C3—C4—H4A109.7
C4—N1—H1C109.2N1—C4—H4B109.7
C1—N1—H1C109.2C3—C4—H4B109.7
Ni1—N1—H1C109.2H4A—C4—H4B108.2
C2—N2—Ni1106.12 (14)N4—C5—C7110.67 (17)
C2—N2—H2C110.5N4—C5—C6108.62 (16)
Ni1—N2—H2C110.5C7—C5—C6111.52 (18)
C2—N2—H2D110.5N4—C5—H5A108.7
Ni1—N2—H2D110.5C7—C5—H5A108.7
H2C—N2—H2D108.7C6—C5—H5A108.7
C3—N3—Ni1110.30 (14)O2—C6—O1124.7 (2)
C3—N3—H3C109.6O2—C6—C5118.49 (19)
Ni1—N3—H3C109.6O1—C6—C5116.77 (17)
C3—N3—H3D109.6C8—C7—C5116.89 (18)
Ni1—N3—H3D109.6C8—C7—H7A108.1
H3C—N3—H3D108.1C5—C7—H7A108.1
C5—N4—Ni1105.55 (12)C8—C7—H7B108.1
C5—N4—H4C110.6C5—C7—H7B108.1
Ni1—N4—H4C110.6H7A—C7—H7B107.3
C5—N4—H4D110.6C10—C8—N6108.74 (19)
Ni1—N4—H4D110.6C10—C8—C7128.0 (2)
H4C—N4—H4D108.8N6—C8—C7123.10 (19)
C9—N5—C10107.7 (2)N6—C9—N5110.9 (2)
C9—N5—H5B126.1N6—C9—H9A124.5
C10—N5—H5B126.1N5—C9—H9A124.5
C9—N6—C8106.13 (18)C8—C10—N5106.5 (2)
C9—N6—Ni1126.91 (15)C8—C10—H10A126.8
C8—N6—Ni1126.83 (14)N5—C10—H10A126.8
N1—C1—C2110.61 (18)C6—O1—Ni1113.91 (14)
N1—C1—H1A109.5HW1—O1W—HW296.1
C2—C1—H1A109.5
N2—Ni1—N1—C4123.43 (15)Ni1—N2—C2—C149.1 (2)
O1—Ni1—N1—C468.40 (14)N1—C1—C2—N252.4 (3)
N4—Ni1—N1—C4145.87 (14)Ni1—N3—C3—C431.7 (2)
N3—Ni1—N1—C420.73 (14)C1—N1—C4—C375.7 (2)
N2—Ni1—N1—C10.79 (14)Ni1—N1—C4—C344.3 (2)
O1—Ni1—N1—C1168.97 (14)N3—C3—C4—N151.5 (3)
N4—Ni1—N1—C191.49 (15)Ni1—N4—C5—C781.26 (17)
N3—Ni1—N1—C1101.91 (15)Ni1—N4—C5—C641.48 (17)
N6—Ni1—N2—C2158.90 (15)N4—C5—C6—O2157.18 (18)
O1—Ni1—N2—C241.5 (4)C7—C5—C6—O280.6 (2)
N4—Ni1—N2—C270.73 (15)N4—C5—C6—O122.2 (2)
N3—Ni1—N2—C2106.72 (15)C7—C5—C6—O1100.0 (2)
N1—Ni1—N2—C226.53 (15)N4—C5—C7—C861.2 (3)
N6—Ni1—N3—C3169.71 (15)C6—C5—C7—C859.8 (3)
N2—Ni1—N3—C374.00 (16)C9—N6—C8—C100.2 (3)
O1—Ni1—N3—C399.34 (15)Ni1—N6—C8—C10175.82 (16)
N4—Ni1—N3—C394.8 (3)C9—N6—C8—C7175.4 (2)
N1—Ni1—N3—C36.16 (15)Ni1—N6—C8—C78.5 (3)
N6—Ni1—N4—C555.03 (13)C5—C7—C8—C10165.6 (2)
N2—Ni1—N4—C5149.92 (13)C5—C7—C8—N619.6 (3)
O1—Ni1—N4—C536.42 (13)C8—N6—C9—N50.2 (3)
N3—Ni1—N4—C541.0 (4)Ni1—N6—C9—N5176.22 (16)
N1—Ni1—N4—C5127.91 (13)C10—N5—C9—N60.5 (3)
N2—Ni1—N6—C969.6 (2)N6—C8—C10—N50.5 (3)
O1—Ni1—N6—C9121.7 (2)C7—C8—C10—N5174.9 (2)
N4—Ni1—N6—C9161.2 (2)C9—N5—C10—C80.6 (3)
N3—Ni1—N6—C932.1 (2)O2—C6—O1—Ni1170.75 (17)
N2—Ni1—N6—C8115.15 (19)C5—C6—O1—Ni19.9 (2)
O1—Ni1—N6—C853.55 (19)N6—Ni1—O1—C660.92 (15)
N4—Ni1—N6—C823.60 (18)N2—Ni1—O1—C656.8 (4)
N3—Ni1—N6—C8143.16 (18)N4—Ni1—O1—C626.84 (14)
C4—N1—C1—C2146.7 (2)N3—Ni1—O1—C6154.22 (15)
Ni1—N1—C1—C228.0 (2)N1—Ni1—O1—C6123.76 (15)
Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1C···O2i0.912.082.968 (3)165
N2—H2C···I1ii0.903.023.843 (3)153
N2—H2D···I1iii0.903.063.882 (2)152
N3—H3C···I1iv0.903.153.894 (2)141
N4—H4C···O2i0.902.373.184 (3)151
N4—H4D···I1iii0.902.873.767 (2)176
N5—H5B···O2v0.862.362.899 (3)121
N5—H5B···I1vi0.863.263.882 (2)132
O1W—HW1···O1vii0.901.842.733 (3)174
O1W—HW2···I1vi0.912.653.537 (2)164
Symmetry codes: (i) x+2, y+2, z+2; (ii) x+1, y+1, z+1; (iii) x, y+1, z; (iv) x+3/2, y+1/2, z+3/2; (v) x1/2, y+3/2, z1/2; (vi) x+1/2, y+1/2, z+3/2; (vii) x1, y, z.

Experimental details

Crystal data
Chemical formula[Ni(C4H13N3)(C6H8N3O2)]I·H2O
Mr460.95
Crystal system, space groupMonoclinic, P21/n
Temperature (K)293
a, b, c (Å)9.384 (5), 15.323 (7), 12.667 (6)
β (°) 108.758 (8)
V3)1724.6 (14)
Z4
Radiation typeMo Kα
µ (mm1)2.93
Crystal size (mm)0.50 × 0.41 × 0.29
Data collection
DiffractometerCCD area detector
diffractometer
Absorption correctionMulti-scan
(SADABS: Sheldrick, 1996; Blessing, 1995)
Tmin, Tmax0.322, 0.483
No. of measured, independent and
observed [I > 2σ(I)] reflections
9823, 3673, 3280
Rint0.018
(sin θ/λ)max1)0.638
Refinement
R[F2 > 2σ(F2)], wR(F2), S 0.022, 0.051, 1.08
No. of reflections3673
No. of parameters192
H-atom treatmentH atoms treated by a mixture of independent and constrained refinement
Δρmax, Δρmin (e Å3)0.60, 0.68

Computer programs: SMART (Bruker, 1998), SMART, SAINT-Plus (Bruker, 1999), SHELXS97 (Sheldrick, 1997), SHELXL97 (Sheldrick, 1997), SHELXTL (Bruker, 1998 ), SHELXTL.

Hydrogen-bond geometry (Å, º) top
D—H···AD—HH···AD···AD—H···A
N1—H1C···O2i0.912.082.968 (3)165.4
N2—H2C···I1ii0.903.023.843 (3)153.4
N2—H2D···I1iii0.903.063.882 (2)152.3
N3—H3C···I1iv0.903.153.894 (2)140.7
N4—H4C···O2i0.902.373.184 (3)151.0
N4—H4D···I1iii0.902.873.767 (2)175.7
N5—H5B···O2v0.862.362.899 (3)121.4
N5—H5B···I1vi0.863.263.882 (2)131.7
O1W—HW1···O1vii0.901.842.733 (3)174.1
O1W—HW2···I1vi0.912.653.537 (2)163.7
Symmetry codes: (i) x+2, y+2, z+2; (ii) x+1, y+1, z+1; (iii) x, y+1, z; (iv) x+3/2, y+1/2, z+3/2; (v) x1/2, y+3/2, z1/2; (vi) x+1/2, y+1/2, z+3/2; (vii) x1, y, z.
 

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